Solve frac{sqrt{x}sqrt[3]{x}}{{x}^frac{-1{4}}}

$$\frac{ \sqrt{ x } \sqrt[3]{ x } }{ { x }^{ \frac{ -1 }{ 4 } } }$$

Differentiate w.r.t. x

$$\frac{13\sqrt[12]{x}}{12}$$

Steps Using Definition of a Derivative

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\sqrt{x}\sqrt[3]{x}}{x^{-\frac{1}{4}}})$$

Factor the expressions that are not already factored in \frac{\sqrt{x}\sqrt[3]{x}}{x^{-\frac{1}{4}}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\sqrt[3]{x}\sqrt{x}}{x^{-\frac{1}{4}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt{x}x^{\frac{7}{12}})$$

Expand the expression.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{13}{12}})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{13}{12}x^{\frac{13}{12}-1}$$

Subtract 1 from \frac{13}{12}.

$$\frac{13}{12}\sqrt[12]{x}$$

Evaluate

$$x^{\frac{13}{12}}$$